Space of modular forms of level 5445, weight 2, and trivial character

• Label: 5445.2.a
• Level: $5445$
• Weight: $2$
• Character orbit: 5445.a
• Rep. character: $\chi_{5445}(1,\cdot)$
• Character field: $\Q$
• Dimension: $181$
• Newform subspaces: $56$
• Sturm bound: $1584$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5445.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(1584\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(23\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5445))\).

	Total	New	Old
Modular forms	840	181	659
Cusp forms	745	181	564
Eisenstein series	95	0	95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(96\)	\(18\)	\(78\)		\(85\)	\(18\)	\(67\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(114\)	\(18\)	\(96\)		\(102\)	\(18\)	\(84\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(108\)	\(18\)	\(90\)		\(96\)	\(18\)	\(78\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(102\)	\(18\)	\(84\)		\(90\)	\(18\)	\(72\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(108\)	\(30\)	\(78\)		\(96\)	\(30\)	\(66\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(102\)	\(25\)	\(77\)		\(90\)	\(25\)	\(65\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(108\)	\(24\)	\(84\)		\(96\)	\(24\)	\(72\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(102\)	\(30\)	\(72\)		\(90\)	\(30\)	\(60\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(408\)	\(85\)	\(323\)		\(361\)	\(85\)	\(276\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(432\)	\(96\)	\(336\)		\(384\)	\(96\)	\(288\)		\(48\)	\(0\)	\(48\)

Trace form

181 * q - q^2 + 175 * q^4 - q^5 - 4 * q^7 - 9 * q^8 - 3 * q^10 - 10 * q^13 - 24 * q^14 + 159 * q^16 + 6 * q^17 - 12 * q^19 - 7 * q^20 - 8 * q^23 + 181 * q^25 + 10 * q^26 + 12 * q^28 - 6 * q^29 + 4 * q^31 - 29 * q^32 + 6 * q^34 + 4 * q^35 - 2 * q^37 + 12 * q^38 - 3 * q^40 + 14 * q^41 - 16 * q^43 + 28 * q^46 - 28 * q^47 + 169 * q^49 - q^50 + 10 * q^52 - 26 * q^53 - 4 * q^56 + 50 * q^58 - 16 * q^59 + 6 * q^61 + 32 * q^62 + 191 * q^64 + 2 * q^65 - 20 * q^67 + 66 * q^68 + 16 * q^70 + 12 * q^71 - 22 * q^73 - 14 * q^74 + 44 * q^76 - 32 * q^79 + q^80 + 82 * q^82 - 14 * q^85 + 32 * q^86 - 42 * q^89 - 48 * q^91 - 4 * q^92 + 76 * q^94 + 12 * q^95 - 114 * q^97 + 55 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5445))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	11
5445.2.a.a	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓	✓			5445.2.a.a	$1$	$2$	\(-2\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.b	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓	✓			5445.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.c	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				15.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{13}+\cdots\)
5445.2.a.d	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				605.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+3q^{7}+3q^{8}+q^{10}+\cdots\)
5445.2.a.e	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				1815.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots\)
5445.2.a.f	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				1815.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
5445.2.a.g	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				1815.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
5445.2.a.h	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				605.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
5445.2.a.i	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				55.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{13}+\cdots\)
5445.2.a.j	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓				1815.2.a.a	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
5445.2.a.k	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓	✓			5445.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.l	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	\(\Q\)	None	✓	✓			5445.2.a.a	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.m	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{2}) \)	None	✓				165.2.a.a	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
5445.2.a.n	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{5}) \)	None	✓	✓			5445.2.a.n	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2q^{7}+\cdots\)
5445.2.a.o	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{5}) \)	None	✓				1815.2.a.f	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
5445.2.a.p	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{5}) \)	None	✓	✓			5445.2.a.n	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.q	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{3}) \)	None	✓				1815.2.a.g	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-\beta q^{7}+4q^{16}-2\beta q^{17}+\cdots\)
5445.2.a.r	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{3}) \)	None	✓				605.2.a.f	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
5445.2.a.s	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{3}) \)	None	✓				165.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}-2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.t	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{3}) \)	None	✓				1815.2.a.h	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.u	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{3}) \)	None	✓				605.2.a.e	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.v	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{5}) \)	None	✓	✓			5445.2.a.n	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+2q^{7}+\cdots\)
5445.2.a.w	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{5}) \)	None	✓	✓			5445.2.a.n	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
5445.2.a.x	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{5}) \)	None	✓				1815.2.a.f	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots\)
5445.2.a.y	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	\(\Q(\sqrt{2}) \)	None	✓				55.2.a.b	$1$	$0$	\(2\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.z	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.148.1	None	✓				165.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ba	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.469.1	None	✓				1815.2.a.l	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bb	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.404.1	None	✓				605.2.a.g	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bc	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.469.1	None	✓				1815.2.a.l	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bd	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.404.1	None	✓				605.2.a.g	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.be	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				165.2.m.a	$1$	$1$	\(-5\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1}+\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bf	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				165.2.m.d	$1$	$1$	\(-3\)	\(0\)	\(-4\)	\(6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bg	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{11 +2 \sqrt{5}})\)	None	✓				55.2.g.a	$1$	$0$	\(-3\)	\(0\)	\(-4\)	\(11\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
5445.2.a.bh	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.48704.2	None	✓				495.2.a.f	$1$	$1$	\(-2\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bi	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				55.2.g.b	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bj	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\zeta_{15})^+\)	None	✓				165.2.m.c	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bk	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{62 -6 \sqrt{5}})\)	None	✓				165.2.m.b	$1$	$1$	\(-1\)	\(0\)	\(4\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5445.2.a.bl	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				1815.2.a.t	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{5}+2\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
5445.2.a.bm	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{3 + \sqrt{6}})\)	None	✓	✓			5445.2.a.bm	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{3}q^{7}+\cdots\)
5445.2.a.bn	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{3 + \sqrt{6}})\)	None	✓	✓			5445.2.a.bm	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots\)
5445.2.a.bo	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{10 +2 \sqrt{13}})\)	None	✓				1815.2.a.s	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots\)
5445.2.a.bp	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				55.2.g.b	$1$	$1$	\(1\)	\(0\)	\(4\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bq	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\zeta_{15})^+\)	None	✓				165.2.m.c	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
5445.2.a.br	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{62 -6 \sqrt{5}})\)	None	✓				165.2.m.b	$1$	$0$	\(1\)	\(0\)	\(4\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bs	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.48704.2	None	✓				495.2.a.f	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bt	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				165.2.m.d	$1$	$0$	\(3\)	\(0\)	\(-4\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bu	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{11 +2 \sqrt{5}})\)	None	✓				55.2.g.a	$1$	$1$	\(3\)	\(0\)	\(-4\)	\(-11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2}-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bv	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				165.2.m.a	$1$	$0$	\(5\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1}-\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bw	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.74043072.1	None	✓	✓			5445.2.a.bw	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
5445.2.a.bx	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.27433728.1	None	✓				605.2.a.m	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{7}+\cdots\)
5445.2.a.by	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.74043072.1	None	✓	✓			5445.2.a.bw	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
5445.2.a.bz	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.437199552.1	None	✓				1815.2.a.y	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ca	$5445$	$2$	5445.a	1.a	$1$	$8$	$8$	$43.479$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		495.2.n.g	$1$	$1$	\(-4\)	\(0\)	\(-8\)	\(8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cb	$5445$	$2$	5445.a	1.a	$1$	$8$	$8$	$43.479$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		495.2.n.g	$1$	$1$	\(-4\)	\(0\)	\(8\)	\(-8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cc	$5445$	$2$	5445.a	1.a	$1$	$8$	$8$	$43.479$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		495.2.n.g	$1$	$0$	\(4\)	\(0\)	\(-8\)	\(-8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
5445.2.a.cd	$5445$	$2$	5445.a	1.a	$1$	$8$	$8$	$43.479$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		495.2.n.g	$1$	$0$	\(4\)	\(0\)	\(8\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5445)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\)\(^{\oplus 2}\)